


"""simple docstring"""



from math import factorial, pi
def      UpperCAmelCase     (       _lowercase :   float			,   _lowercase :   int = 3_0	)						-> float:


	"""simple docstring"""




	if not isinstance(_lowercase			,   (int, float)	):
		raise ValueError('''maclaurin_sin() requires either an int or float for theta'''	)

	if not isinstance(_lowercase			,   _lowercase	) or accuracy <= 0:
		raise ValueError('''maclaurin_sin() requires a positive int for accuracy'''	)

	lowerCAmelCase_      							=			float(_lowercase	)
	lowerCAmelCase_      							=			theta // (2 * pi)
	theta -= 2 * div * pi
	return sum(
	    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1	) for r in range(_lowercase	)	)
def      UpperCAmelCase     (       _lowercase :   float			,   _lowercase :   int = 3_0	)						-> float:


	"""simple docstring"""




	if not isinstance(_lowercase			,   (int, float)	):
		raise ValueError('''maclaurin_cos() requires either an int or float for theta'''	)

	if not isinstance(_lowercase			,   _lowercase	) or accuracy <= 0:
		raise ValueError('''maclaurin_cos() requires a positive int for accuracy'''	)

	lowerCAmelCase_      							=			float(_lowercase	)
	lowerCAmelCase_      							=			theta // (2 * pi)
	theta -= 2 * div * pi
	return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r	) for r in range(_lowercase	)	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		print(maclaurin_sin(10))
		print(maclaurin_sin(-10))
		print(maclaurin_sin(10, 15))
		print(maclaurin_sin(-10, 15))

		print(maclaurin_cos(5))
		print(maclaurin_cos(-5))
		print(maclaurin_cos(10, 15))
		print(maclaurin_cos(-10, 15))



"""simple docstring"""



from collections.abc import Sequence
from queue import Queue







class    __a						:







				def __init__( self      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase=None      ,	UpperCAmelCase=None   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			start
					lowerCAmelCase_      							=			end
					lowerCAmelCase_      							=			val
					lowerCAmelCase_      							=			(start + end) // 2
					lowerCAmelCase_      							=			left
					lowerCAmelCase_      							=			right







				def __repr__( self   ):

					'''simple docstring'''






					return F"""SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"""







class    __a						:







				def __init__( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			collection
					lowerCAmelCase_      							=			function
					if self.collection:
						lowerCAmelCase_      							=			self._build_tree(0      ,	len(UpperCAmelCase   ) - 1   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					self._update_tree(self.root      ,	UpperCAmelCase      ,	UpperCAmelCase   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					return self._query_range(self.root      ,	UpperCAmelCase      ,	UpperCAmelCase   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if start == end:
						return SegmentTreeNode(UpperCAmelCase      ,	UpperCAmelCase      ,	self.collection[start]   )
					lowerCAmelCase_      							=			(start + end) // 2
					lowerCAmelCase_      							=			self._build_tree(UpperCAmelCase      ,	UpperCAmelCase   )
					lowerCAmelCase_      							=			self._build_tree(mid + 1      ,	UpperCAmelCase   )
					return SegmentTreeNode(UpperCAmelCase      ,	UpperCAmelCase      ,	self.fn(left.val      ,	right.val   )      ,	UpperCAmelCase      ,	UpperCAmelCase   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if node.start == i and node.end == i:
						lowerCAmelCase_      							=			val
						return
					if i <= node.mid:
						self._update_tree(node.left      ,	UpperCAmelCase      ,	UpperCAmelCase   )
					else:
						self._update_tree(node.right      ,	UpperCAmelCase      ,	UpperCAmelCase   )
					lowerCAmelCase_      							=			self.fn(node.left.val      ,	node.right.val   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if node.start == i and node.end == j:
						return node.val

					if i <= node.mid:
						if j <= node.mid:
							# range in left child tree
							return self._query_range(node.left      ,	UpperCAmelCase      ,	UpperCAmelCase   )
						else:
							# range in left child tree and right child tree
							return self.fn(
							    self._query_range(node.left      ,	UpperCAmelCase      ,	node.mid   )      ,	self._query_range(node.right      ,	node.mid + 1      ,	UpperCAmelCase   )      ,	)
					else:
						# range in right child tree
						return self._query_range(node.right      ,	UpperCAmelCase      ,	UpperCAmelCase   )







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					if self.root is not None:
						lowerCAmelCase_      							=			Queue()
						queue.put(self.root   )
						while not queue.empty():
							lowerCAmelCase_      							=			queue.get()
							yield node

							if node.left is not None:
								queue.put(node.left   )

							if node.right is not None:
								queue.put(node.right   )


if __name__ == "__main__":
		import operator

		for fn in [operator.add, max, min]:
				print('*' * 50)
				lowercase_							=							SegmentTree([2, 1, 5, 3, 4], fn)
				for node in arr.traverse():
						print(node)
				print()

				arr.update(1, 5)
				for node in arr.traverse():
						print(node)
				print()

				print(arr.query_range(3, 4))  # 7
				print(arr.query_range(2, 2))  # 5
				print(arr.query_range(1, 3))  # 13
				print()